Thabit number

An integer of the form 32n-1, or 2n+1+2n-1. They are listed in A055010 of Sloane’s OEIS. The Thabit numbers are a subset of the Proth numbers.

The mathematician and astronomer Thabit ibn Qurra studied these numbers in search of a formula for amicable pairs. He found that when two consecutive Thabit numbers are also prime numbersMathworldPlanetmath (corresponding to indices n and n-1) and 922n-1-1 is a prime number, too, then these numbers multiplied by 2n will reveal an amicable pair. The only n known to fit these criteria are 2, 4 and 7. The largest Thabit number known to be prime corresponds to index 2312734, its immediate lower neighbor is composite.

It is conjectured that the nimfactorial of a Thabit number is always 2.

Title Thabit number
Canonical name ThabitNumber
Date of creation 2013-03-22 15:52:58
Last modified on 2013-03-22 15:52:58
Owner Mravinci (12996)
Last modified by Mravinci (12996)
Numerical id 5
Author Mravinci (12996)
Entry type Definition
Classification msc 11A05
Synonym Thabit ibn Kurra number
Synonym Thabit ibn Kurrah number
Synonym Thabit ibn Qurra number
Synonym Thabit ibn Qurrah number
Synonym Thabit bin Kurra number
Synonym Thabit bin Kurrah number
Synonym Thabit bin Qurra number
Synonym Thabit bin Qurrah number
Related topic AFormulaForAmicablePairs